Atmospheric_Dynamics_III-primitive-eq_continuity-v4

Atmospheric_Dynamics_III-primitive-eq_continuity-v4 -...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Primitive Equations PRIMITIVE EQUATIONS
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Definition The so called primitive equations are those that govern the evolution of the large-scale motions. In other words, are the equations that describe the horizontal and vertical movement of the atmosphere and changes in temperature They are easiest to interpret when we transform the z coordinate into p coordinate
Image of page 2
Vertical movement in p- coordinates The vertical velocity component in (x,y,p) coordinate is z p w p t p dt dp + + = V ϖ V- horizontal wind Substituting ( δ p/ δ z )=- ρ g from the Hydrostatic equation: gw ρ ϖ - 2245 gw p t p ρ ϖ - + = V 10hPa/day 100hPa/day <<10hPa/day ~ 1 week for a parcel to move from the lower to the upper troposphere Note that w and ω have opposite sign: ascending (descending) movements ω negative (positive)
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
How to interpret ω Pressure ω = d p / d t 1000mb 900mb 800mb 700mb 600mb
Image of page 4
Comparing w with ω 100hPa/day is equivalent to 1km/day or 1cm/s in the lower troposphere and twice that value in the midtroposphere (see the example shown before) (the distance between two pressure levels increases with height)
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Hydrostatic balance We saw before (Joel’s classes) that the vertical component of the movement could be described as: z z F C g z p dt dw + + - - = ρ 1 Where Cz are the vertical components of the Coriolis and Frictional forces, respectively Vertical velocities are very small and we can assume to within ~1% that the upward gradient force balances the downward pull of gravity also for large-scale motions (this approach is not valid for cloud-scale motions though). The Hydrostatic Balance can be assumed
Image of page 6
Thermodynamic Energy Equation The evolution of the weather systems is governed by dynamical (Newton’s Laws) AND THERMODYNAMIC PROCESSES (First and second law of thermodynamics) The first law of the Thermodynamics (which represents changes and heat, expansion/contraction, increase/decrease in temperature, etc) is a prognostic equation for the parcel of air moving in the atmosphere
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
First Law of Thermodynamics The first Law of the Thermodynamics can be written as: dp dT c dt J p α - = Where J represents the DIABATIC HEATING RATE (Joules kg-1 s-1 ) and dt is the infinitesimal time interval. Dividing by dt and rearranging the terms we obtain: J dt dp dt dT c p + = α Using the state equation for a substitution of α and replacing / dp dt by ω we obtain the thermodynamic energy equation p c J p T dt dT + = ϖ κ κ = R/cp=0.286
Image of page 8
Interpretations (1) Rate of change of temperature due to ADIABATIC EXPANSION OR COMPRESSION .
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern